Truncating first-order Dyson-Schwinger equations in Coulomb-Gauge Yang-Mills theory
arXiv:0905.4594 · doi:10.1007/s00601-009-0073-0
Abstract
The non-perturbative domain of QCD contains confinement, chiral symmetry breaking, and the bound state spectrum. For the calculation of the latter, the Coulomb gauge is particularly well-suited. Access to these non-perturbative properties should be possible by means of the Green's functions. However, Coulomb gauge is also very involved, and thus hard to tackle. We introduce a novel BRST-type operator r, and show that the left-hand side of Gauss' law is r-exact. We investigate a possible truncation scheme of the Dyson-Schwinger equations in first-order formalism for the propagators based on an instantaneous approximation. We demonstrate that this is insufficient to obtain solutions with the expected property of a linear-rising Coulomb potential. We also show systematically that a class of possible vertex dressings does not change this result.
22 pages, 4 figures, 1 table
References in corpus (41)
- The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
- Infrared Properties of QCD from Dyson-Schwinger equations
- Unified description of light- and strange-baryon spectra
- Non-perturbative Landau gauge and infrared critical exponents in QCD
- Coulomb Gauge QCD, Confinement, and the Constituent Representation
- Variational solution of the Yang-Mills Schrödinger equation in Coulomb gauge
- Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory
- No confinement without Coulomb confinement
- Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory II
- Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory
- Effective Q-Q Interactions in Constituent Quark Models
- Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
- Coulomb Energy, Vortices, and Confinement
- Light Baryons in a Constituent Quark Model with Chiral Dynamics
- Coulomb gauge gluon propagator and the Gribov formula
- Running Coupling in Non-Perturbative QCD - I. Bare Vertices and y-max Approximation
- Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge
- Two-loop Improved Truncation of the Ghost-Gluon Dyson-Schwinger Equations: Multiplicatively Renormalizable Propagators and Nonperturbative Running Coupling
- Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory
- Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge
- QCD in the Infrared with Exact Angular Integrations
- Quark-Model Identification of Baryon Ground and Resonant States
- The infrared behavior of Landau gauge Yang-Mills theory in d=2, 3 and 4 dimensions
- Renormalizable Non-Covariant Gauges and Coulomb Gauge Limit
- Numerical Study of Gluon Propagator and Confinement Scenario in Minimal Coulomb Gauge
- Algorithmic derivation of Dyson-Schwinger Equations
- Renormalization-group Calculation of Color-Coulomb Potential
- Propagator Dyson-Schwinger Equations of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism
- Two-Point Functions of Coulomb Gauge Yang-Mills Theory
- Analytic calculation of color-Coulomb potential and color confinement
- Fit to Gluon Propagator and Gribov Formula
- Perturbation Theory of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism
- Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory
- Infrared Behaviour and Running Couplings in Interpolating Gauges in QCD
- Resolving temporal Gribov copies in Coulomb gauge Yang-Mills theory
- Hamiltonian Approach to 1+1 dimensional Yang-Mills theory in Coulomb gauge
- Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory
- Landau Gauge QCD: Functional Methods versus Lattice Simulations
- Infrared-suppressed gluon propagator in 4d Yang-Mills theory in a Landau-like gauge
- The Yang-Mills Vacuum in Coulomb Gauge in D=2+1 Dimensions
- Quark and gluon confinement in Coulomb gauge
Cited by in corpus (10)
- The QCD Running Coupling
- Gauge bosons at zero and finite temperature
- Leading order infrared quantum chromodynamics in Coulomb gauge
- Hamiltonian Flow in Coulomb Gauge Yang-Mills Theory
- Towards a Born term for hadrons
- The Gribov horizon and the one-loop color-Coulomb potential
- Bound states at lowest order in hbar
- The Coulomb flux tube on the lattice
- Schwinger-Dyson Equations in Coulomb Gauge Consistent with Numerical Simulation
- Instantaneous Dynamics of QCD